[talanum1 (OP)]

Yes, some of them can be proven using axioms of operators called Stoppers and Attractors. See my manuscript at: https://www.ijasr.org/paper/IJASR0042515.pdf.

[Bored chemist]

axioms of operators called Stoppers and Attractors.

Are these provable?

(Or is it turtles all the way down?)

[talanum1 (OP)]

Are these provable?

(Or is it turtles all the way down?)

Not as far as I know. They are unlikely to be provable but intuitively apply the notions of "attraction", "repulsion" and "stopping attraction".

Turtles all the way down can mean: axioms all the way down - I don't know.

[Bored chemist]

So, what you have  said is that, if we assume a set of axioms we no longer need to assume a different set of axioms.

That hardly seems to help.

[talanum1 (OP)]

So, what you have  said is that, if we assume a set of axioms we no longer need to assume a different set of axioms.

Using the most basic axioms, we don't need the higher level axioms any more.

The fact that Attractors and Stoppers (nearly) pushes back the axioms one level is amazing. It also proves the inference Rules: Modus Ponens and AND-introduction.